Sprint Nextel shares have outperformed Apple this year, along with all but one other stock in the Standard & Poor’s 500 index. Can this be real?

“I tell the team here, ‘You’re not going to see any mission accomplished signs anywhere on this campus,’” CEO Dan Hesse said in an interview from his office in Overland Park.. “This is a long process.”

In his five years running Sprint, Hesse has worked to fix the mess he was handed after the $36 billion purchase of Nextel failed and 7.7 million monthly subscribers fled the carrier. Though he has had his own struggles, such as a turbulent joint venture with Clearwire and a foray into dead-end WiMax technology, he predicts that Sprint is on track to return to profit growth in 2014, following seven years of losses.

Some analysts agree — with reservations.

“One thing that keeps people skeptical is that we’ve seen these head fakes before,” said Phil Cusick, an analyst with JPMorgan Chase & Co. in New York. “There’s no one on Wall Street who has been around for a while that hasn’t lost money on Sprint.”

Sprint’s challenges remain daunting. It’s a distant third to Verizon Wireless and AT&T in customers, and the bigger rivals have more extensive LTE networks, letting them offer speedier service to customers across the nation. Even if Sprint turns the corner in 2014, it will have suffered almost $50 billion in losses over a seven-year stretch, including estimated losses for 2012 and 2013.

Despite all that, Cusick has a buy rating on the stock. With Sprint shares up more than 140 percent this year, Wall Street has shown increasing faith in the comeback. A year ago, investors were concerned the company would crack under the pressure of a $7 billion network upgrade plan and a costly bargain to get the iPhone, a deal that requires Sprint to buy $15.5 billion worth of devices from Apple.

Since then, Sprint has gotten bigger benefits than expected from the iPhone, both by helping it attract customers away from other carriers and by boosting the size of users’ phone bills. Sprint also delivered on its promise to introduce a speedy LTE network in at least six cities this summer. LTE, short for long- term evolution, is being added to 100 more cities.

“A year ago, management was talking about all the things they needed to do — it was hard to listen to them, they had so little credibility,” said Scott Dinsdale at Montpelier, Vt.-based KDP Investment Advisors, which owns Sprint bonds. “You just held your nose and held the bonds. Now they’ve gotten to the point where you can see light at the end of the tunnel.”

Sprint shares Monday rose 5 cents to $5.70. In the S&P 500 this year, the stock is second only to PulteGroup, the Bloomfield Hills, Mich.-based homebuilder.

Sprint gained renown as an upstart long distance competitor in the 1980s, when it touted a fiberoptic network with pin drop clarity. After shifting its focus to the wireless market, the company pursued the Nextel Communications acquisition in 2005. Gary Forsee, then the CEO, saw the deal as a way to compete with the industry’s big two — AT&T and Verizon. Instead, network glitches and customer service complaints put Sprint further behind.

Nextel’s network had 16.1 million customers when it was acquired. That number had plunged to 4.4 million as of June. In 2007, less than three years after the Nextel deal, Forsee was forced out by the board and Hesse was hired.

Forsee, who served as president of the University of Missouri for three years after leaving Sprint, declined to comment.

Hesse, a lanky 58-year-old who prefers to work in jeans, said he is orchestrating Sprint’s turnaround in three stages.

The past four years have been a recovery period.

This year and next, he said, are the investment phase. That’s when Sprint dismantles the outdated Nextel network and installs LTE technology.

“Right now, we are spending money like crazy revamping the network,” he said.

Adding to the costs are the heavy iPhone subsidies, an expense to acquire lots of customers that will “pay off longer term,” he said.

Stage three will be Sprint’s growth phase, when these improvements begin to flow to the company’s bottom line. Sprint will see profit margin expansion and earnings growth in 2014, Hesse said.

Sprint’s shares have beat the S&P 500 by 123 percent this year. Before 2012, the stock had underperformed the index by 86 percent since the beginning of 2007.

The transformation has hinged in part on slimming down the company. When Hesse took over in December 2007, Sprint had 60,000 employees. Today it has a third fewer, about 40,000.

The diminished ranks are evident at its leafy headquarters, a $1 billion complex of brick and marble-column buildings that looks like a college campus in July. Built during the late-1990s Internet boom to hold 14,500 employees, it houses 6,500.

A return to profitability in 2014 is no sure thing. Analysts predict that Sprint will be right around the break-even point that year, though they do see the company solidly in the black by 2015, according to data compiled by Bloomberg.

“There’s still a considerable amount of risk in Sprint since they are not quite halfway through the network migration,” Dinsdale said. “They are chronic in their disappointments.”

When Sprint acquired Nextel, it promised seamless “interoperability” between the two networks. Instead, the deal saddled Sprint with incompatible technology that forced Hesse to cut the losses and shut it down. Sprint ended up writing off about $30 billion, or 80 percent of the purchase price.

Now Sprint has to coax those customers onto its main network. Initially the company had been converting about 25 percent of defecting Nextel customers into Sprint users. By last quarter, after focusing more intently on courting those subscribers, the company’s recapture rate rose to 60 percent.

Higher retention will help slow the loss of customers, though the company will continue to post user losses until the Nextel network is shut down next year, Hesse said. Sprint also may eventually drop Nextel from its corporate name, he said.

Then there’s Clearwire. Without enough money to build its own national fourth-generation network, Sprint contributed some of its airwaves to a joint venture with Clearwire in May 2008. Comcast, Time Warner Cable, Google and Intel also invested in the business, which planned to use WiMax technology to build a fast, national wireless service. The venture has yet to break even, and it stopped its WiMax expansion last year to focus instead on LTE.

Next month will be the anniversary of Sprint’s stormy 2011 analysts day, when it refused to share information about the iPhone purchase agreement and the impact on finances. Sprint further irked investors by saying it would have to raise more money to fund its network upgrade plan. The shares fell the most in three years, dropping 26 percent over a two-day period.

The company later agreed to share more data about the iPhone, and the Apple deal is now seen as a smart move. Sprint may look even smarter a year from now, when the LTE network is more complete and the full impact of the company’s deal with Apple is known, Dinsdale said.

“It was a huge transaction — it was transformational,” Dinsdale said. “But it needed to be done and they had the guts to do it.”